Abstract
Establishing accurate as well as interpretable models of network activity is an open challenge in systems neuroscience. Here we infer an energy-based model of the ARTR, a circuit that controls zebrafish swimming statistics, using functional recordings of the spontaneous activity of hundreds of neurons. Although our model is trained to reproduce the low-order statistics of the network activity at short time-scales, its simulated dynamics quantitatively captures the slowly alternating activity of the ARTR. It further reproduces the modulation of this persistent dynamics by the water temperature and visual stimulation. Mathematical analysis of the model unveils a low-dimensional landscape-based representation of the ARTR activity, where the slow network dynamics reflects Arrhenius-like barriers crossings between metastable states. Our work thus shows how data-driven models built from large neural populations recordings can be reduced to low-dimensional functional models in order to reveal the fundamental mechanisms controlling the collective neuronal dynamics.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
We include a systematic cross-validation of the inferred models following the comments by Reviewer. We show the predictions of the model (for observables such as the mean activity and the pairwise correlations, and for log-likelihoods) in the figures on the main text, e.g. figure 3A, as well as in the appendix figure 3. We explain why we have fitted a model for each water temperature and each fish, and carry out a systematic comparison of the models inferred at different water temperatures for the same fish. We have added a new figure 3B to show the absence of correlation between models corresponding to different water temperatures. We have also included a new section in the Discussion to better discuss the role of temperature on the activity. We have also slightly rewritten the introduction of the model in the Results section to better distinguish the notions of water temperature and model temperature (implicitly set by the amplitude of the J,h parameters), as our first manuscript could be confusing on this point. point out the exact figure in Dunn et al., Elife 2016 in which the authors demonstrate that the sign of the difference in activity of the right and left ARTR populations dictates the swim direction. Replicating these observations would thus be redundant but would also require a different and more complex experimental setup. Indeed, they were obtained by recording fictive turns using electrical recordings from peripheral motor nerves in paralyzed larvae, as actual tail bouts tend to occur at very low frequency in tethered configurations.
